What is the "do-nothing" convolution kernel

Question

If I am trying to do a convolution kernel in Frequency space - what is the "do-nothing" kernel. In other words, if I view the image after applying the kernel, and normalizing it in Frequency space, I just want to see the raw Fourier transform

Is it the identity matrix? my kernel is 3x3

Thanks

Answer 1

A do-nothing 3x3 kernel will be:

0 0 0
0 1 0
0 0 0

I hope I understood your question correctly - I'm not sure why you would want such a kernel, when it's much easier to just skip the convolution entirely.

Answer 2

The "do-nothing" convolution kernel is the delta-dirac function: "δ(x)".

The solution mark-ransom shared is just that! Any signal convolved with the delta-dirac is identical to the original signal. This applies to convolution in any n-dimension.

The delta-dirac has many other interesting properties:

• δ can be discrete or continuous in nature
• δ(0) = ∞
• The laplace transform of δ(x) equals 1
• The indefinite integral of δ(x) equals 1
• see Wikipedia for more

Also see how to create δ convolutional neural network layer